Open AccessLife games and statistical models.
Author(s) -
Max Dresden,
David Wong
Publication year - 1975
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.72.3.956
Subject(s) - nonlinear system , formalism (music) , class (philosophy) , set (abstract data type) , mathematics , dynamic equation , mathematical economics , computer science , physics , artificial intelligence , art , musical , quantum mechanics , visual arts , programming language
A set of equations is obtained, which describes the rules of a class of games (life games). These games simulate the processes of growth, death, survival, and competition. The equations are nonlinear difference equations, where the degree of nonlinearity is directly related to the number of interacting neighbors. The time evolution and the development of geometric patterns can be studied starting from these equations. Extensions and generalizations, such as the introduction of stochastic elements, can easily be accommodated in the formalism. Some significant unsolved problems are noted.